TY - JOUR

T1 - Asymptotic boundary layer method for unstable trajectories : Semiclassical expansions for individual scar wavefunctions.

AU - Vagov, A.

AU - Schomerus, Henning

AU - Zalipaev, V.

PY - 2009/11

Y1 - 2009/11

N2 - We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wave functions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field.

AB - We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wave functions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field.

U2 - 10.1103/PhysRevE.80.056202

DO - 10.1103/PhysRevE.80.056202

M3 - Journal article

VL - 80

SP - 056202

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 5

ER -